Let N, Φ) be a finite circular Ferrero pair. We define the disk with center b and radius a, D(a;b), as D (a; b) = x ∈ Φ(r)+c pipe r ≠ 0, b ∈ Φ (r)+c, pipe(Φ (r)+c) ∩ (Φ(a)+b)pipe=1. Using this definition we introduce the concept of interior part of a circle, Φ(a)+b, as the set I(Φ (a)+b)= D (a; b) \ (Φ (a)+b). Moreover, if BDis the set of all disks, then, in some interesting cases, we show that the incidence structure (N, BD, ∈) is actually a balanced incomplete block design and we are able to calculate its parameters depending on pipeNpipe and pipeΦpipe. © 2012 Springer Basel.

BIB-Designs from Circular Nearrings

BENINI, ANNA;Frigeri, Achille;
2013-01-01

Abstract

Let N, Φ) be a finite circular Ferrero pair. We define the disk with center b and radius a, D(a;b), as D (a; b) = x ∈ Φ(r)+c pipe r ≠ 0, b ∈ Φ (r)+c, pipe(Φ (r)+c) ∩ (Φ(a)+b)pipe=1. Using this definition we introduce the concept of interior part of a circle, Φ(a)+b, as the set I(Φ (a)+b)= D (a; b) \ (Φ (a)+b). Moreover, if BDis the set of all disks, then, in some interesting cases, we show that the incidence structure (N, BD, ∈) is actually a balanced incomplete block design and we are able to calculate its parameters depending on pipeNpipe and pipeΦpipe. © 2012 Springer Basel.
balance incomplete block design; Finite field; planar nearring; Mathematics (miscellaneous); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1063818
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